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ACROSS
1 Immoral woman arrested, beheaded (6) WICKED {W}{pICKED}
4 Most primitive, mischievous lady in a corner sits oddly (8) SIMPLEST {IMP}{L} in {SE} with {SiTs}
9 Crooked and heartless lackey in government... (5) LYING {La..eY}{IN}{G}
10 ...likely candidate, contesting in the front, looter, corrupt officer (9) COLLECTOR {Li...y+Ca...e+Co...g+LOOTER}
11 Arranged funding to back liberal (4) LAID {AID}<=>{L}
12 Advances in the absence of leader to borders (4) ENDS lENDS
13 Whipped, took some broth out and consumed (5) EATEN bEATEN
15 Say, match starting late, female ahead against rival (7) FIGHTER {lIGHTER}<=>{F}
16 Travel free winning agent's heart (4) RIDE {RID}{agEnt}
19 Dog's tail at the tip is short (4) CURT {CUR}{Tail}
20 Twisted plot in the climax directed (7) TANGLED {ploT}{ANGLED}
23 Party with nurse (5) TREAT [DD]
24 Beast found in Kigali only (4) LION [T]
25 You being old, should be out partying without husband (4) THOU {T{H}OU*}
27 Say program at America showcasing essence of karate framework (9) APPARATUS {APP}{US} over {kARATe}
28 Rehab itinerary can contain addiction (5) HABIT [T]
29 Distribution of shares covers small quantity; innocuous (8) HARMLESS {HAR{ML}ESS*}
30 One is not welcome? Rips the heart out (6) UNITED UNInviTED
DOWN
1 File on fauna (8) WILDLIFE {FILE}* [RA]
2 Gin, ice mixed with some lime's surely at the top of limits (8) CEILINGS {GIN+ICE+Li..s+Su...y}*
3 Urges two girls to participate in English class finally (4) EGGS {E}{GG}{c..sS}
5 Pictures are fantasies describing art forms over time (13) ILLUSTRATIONS {ILLUS{ART*}{T}IONS}
6 Claiming to interpret end in Godfather frames (10) PRETENDING [T]
7 Property in East and West Bengal perhaps (6) ESTATE {E}{STATE}
8 Leaders from the high ranks oppose Narendra enshrining the seat of power (6) THRONE Acrostic
10 Compliments Carol aunt, gets misconstrued (13) CONGRATULATES*
14 Ditch behind street gets filled by some cement, guard often takes a look in the front concerned with the building (10) STRUCTURAL {RU{Ce...t}T}<=>{ST} and {gUaRd}{A}{Look}
17 Letters from a leading physicist in the lab dispersed (8) ALPHABET {A}{THE+LAB}* over {Ph...t}
18 Changed advertisement on fair's starting & ending of Eid (8) ADJUSTED {AD}{JUST}{EiD}
21 Link for dirty chat after a payment finally (6) ATTACH {CHAT}*<=>{A}{p...nT}
22 After losing opener, perhaps MS Dhoni gets down in place? More mysterious (6) DEEPER (-k+d)DEEPER
26 Poor husband came into money (4) THIN {T{H}IN}
Reference List
Woman = W, Lady = L, Corner = SE, Government = G, Liberal = L, Female = F, Husband = H, Girl = G, Time = T, East = E, Street = ST, Down = D, Husband = H