Direct Action by Hubris

For a puzzle whose only theme was an entry method to be discovered, this was remarkably challenging. The extra words in the clues were by no means easy to spot, and even when found they initially didn't seem to help much. Until the rule governing grid entry could be determined, cross-checking letters were of little help, so the solver was left with the task of solving most clues blind. Eventually, for Gregson, the first letters of the extra words seemed to spell out "Grid entries must conform literally...", which still wasn't much help.

Finally, realising that another pass through the extra words might yield a more informative message, he found that the fourth letters in sequence completed the rule thus: Grid entries must conform literally to their direction, i.e. north to south, or west to east, or vice versa". Thus was revealed that entries could be reversed and that the direction of each entry would give a transformation such as "N to S", meaning that a north-to-south entry would get each N replaced with S. Once this rule was established it was a relatively straightforward matter to fill in the grid.

Across
1 [Graceful] bird, last of four seen in congested city (4)
WREN (Last letter of FOUR inside WEN)
4 Cockney has news about tangled nets and promises [retribution] (8)
EARNESTS (Jumble NETS inside 'EARS (Cockney HEARS))
10 [Indian] tax assessor in distressed torments having lost money (7)
STENTOR (Jumble TORMENTS minus M(oney))
11 Pliant lecturer in [decorous] decline (5)
WANLE (L(ecturer) inside WANE)
13 Tips off [Etonian] knight in contests (5)
WARNS (N (knight) inside WARS)
14 Fools around with [native] birds (5)
TWITS (W(ith) inside TITS)
16 [Token] offence about English poet's descendant (4)
SIEN (E(nglish) inside SIN)
17 Present front of [Roundhead's] large pate (4)
NOWL (NOW + first letter of LARGE)
L by itself might be considered to be indicated by "large", making "front of" redundant, but Chambers does not support this abbreviation.
18 Starts again on all [important] points (6)
RENEWS (RE + four compass points)
20 Responded to reorganisation of war [emergency] needs (8)
ANSWERED (Anag. WAR NEEDS)
25 We turned pink possibly as a [Scottish] member of an underground organisation (8)
WEREWOLF (WE + FLOWER rev.)
28 Clumsy lassie [might] whip pastry (6)
TAWPIE (TAW + PIE)
30 [Unstable] ice field ends brief sail to Skye (4)
FLOE (Last letters of BRIEF SAIL TO SKYE)
32 Start to tame a [strong] temper (4)
TONE (First letter of TAME + ONE)
34 Get up about noon for [Tuesday's] wash (5)
RINSE (N(oon) inside RISE)
36 Climber involved in Australian [colonial] expeditions (5)
LIANE (Hidden in AustraLIAN Expeditions)
37 Projecting edges formed by lopped [ombu] foliage (5)
EAVES (LEAVES minus first letter)
38 Ducks surrounding pintail's first [nesting] pairs (7)
SPOUSES (First letter of PINTAL inside SOUSES)
39 [Fashionable] trifles, perhaps strained over (8)
DESSERTS (STRESSED rev.)
Fun to see this well-known reversal as a Listener clue, well concealed by the extra word.
40 Overcame the onset of third-rate [Oxford] habit (4)
WONT (WON + first letter of THIRD-RATE)

Down
1 Edmund's food [refreshed] old-time ox (7)
PASTURE (PAST + URE (ox))
2 Take an old [mid-western] copying machine (5)
RONEO (R (recipe = take) + ONE + O(ld))
3 Drinking cup appeared in ancient [legend] as sacred (4)
TASS (Hidden in ancienT AS Sacred)
4 Once beat [Irish] three-quarter in Southern League's final (6)
SWINGE (S + WING + last letter of LEAGUE)
Chambers does not really support WING as a synonym for THREE-QUARTER but various Rugby formation websites did so.
5 A card game [that] is a card game (4)
SNAP (S (is) + NAP)
6 Widely cover a fish pond in [eastern] river? No, the other way round (5)
STREW (R(iver) inside STEW)
7 Tropical shrubs without [recorded] name so far (6)
SENNAS (SEN (without) + N(ame) + AS)
8 Mountainous cask held by possibly stout [attendant] (6)
ALPINE (PIN inside ALE)
9 A [local] smoked sausage from small Scottish city (5)
WEENY (WEE + NY (New York))
12 Insane [lassie] mixed colour (6)
SIENNA (Anag. INSANE)
15 English bishop, sober [youth] at first, goes astray (4)
ERRS (E(nglish) + RR (bishop) + first letter of SOBER)
19 Nap set back [through] being around bedlam (6)
SNOOZE (ZOO inside ENS, all rev.)
A simple clue made almost unfathomable by the extra word and the easy-to-miss significance of "being".
21 Dry wind passage in uninteresting [opera] (4)
SERE (Hidden, reversed, in unintERESting)
22 A fine head? A [slight] travesty (7)
AFFRONT (A + F(ine) + FRONT)
FRONT = HEAD seemed a bit questionable.
23 Time to know [holiday] sun breaks (6)
TWISTS (T + WIST + S(un))
24 Shrinks Americans' [execrable] blouses, one hears (6)
WASTES (Homophone WAISTS)
26 Wrap up [internationalism] in French conceit (6)
ENWIND (EN (French IN) + WIND))
27 Birds singing: warblers, [reeves] and northern skylarks started off (5)
SWANS (First letters of SINGING WARBLERS AND NORTHERN SKYLARKS)
29 Man, having enclosed river, [dives] for shellfish (5)
PRAWN (R(iver) inside PAWN)
31 Special quiet [intruders] move stealthily to plunder (5)
SPOIL (S(pecial) + P (quiet) + OIL)
33 Pool made of [Russian] material out east (4)
LINN (LINEN minus E)
35 Island close to [equator] once containing university (4)
NUIE