Another easy one, lots of anagrams and containments. Probably also reasonable beginner crossword fodder!

Across

1

Report mimic used in public relations (5)
PAPER — APE (mimic) in PR (public relations)

4

Bus involved in crash is OK (6-2)
THUMBS-UP — anagram (involved) of BUS inside THUMP (crash)

10

Authority's men control gavel when gaining order (5,10)
LOCAL GOVERNMENT — anagram (when gaining order) of MEN CONTROL GAVEL

11

Knowledgeable media bosses supporting reshuffle of ACTU? (8)
EDUCATED — ED ED (media bosses) containing anagram (reshuffle) of ACTU

12

Time taken by crew unsettled hard and despicable person (6)
WRETCH — anagram (unsettled) of CREW containing T (time), H (hard)

14

Chauvinist's old partner is spotted in street (6)
SEXIST — ST (street) containing EX (old partner) IS

15

Renoir remixed last bit of colour by mistake (2,5)
IN ERROR — anagram (remixed) of RENOIR, R (last letter of colour)

18

Support a form of identification (3)
AID — A ID (form of identification)

19

Cold executioner, a reformist (7)
CHANGER — C (cold) HANGER (executioner)

21

Queen of Persia rules the region to some extent (6)
ESTHER — hidden in rulES THE Region

24

An advance made by the French republic in Africa (6)
ANGOLA — AN GO (advance) LA (the French)

26

Various sites carrying small items of confectionery (8)
SWEETIES — anagram (various) of SITES containing WEE (small)

28

Stolen app, integrated into radio, permits broadcast (15)
MISAPPROPRIATED — APP inside anagram (broadcast) of RADIO PERMITS

29

Disciplined consumer checking radio band width (8)
DIAMETER — DIETER (disciplined consumer) containing AM (radio band)

30

Body's core temperature approximately (5)
TORSO — T (temperature) OR SO (approximately)

Down

1

Everyone invested in pet's bed (6)
PALLET — PET containing ALL (everyone)

2

One court shown in wholesome movie (7)
PICTURE — PURE (wholesome) containing I CT (court)

3

Redeployed General is letting go (9)
RELEASING — anagram (redeployed) of GENERAL IS

5

Digger's ring accepted by the girl (4)
HOER — HER (the girl) containing O (ring)

6

Contents of bedroom, an ordinary house and property (5)
MANOR — hidden in bedrooM AN ORdinary

7

Horses at the back race and suffer in the heat (7)
SWELTER — S (last letter of horses) WELTER (race)

8

Tossers disturbed priest outside church (8)
PITCHERS — anagram (disturbed) of PRIEST outside CH (church)

9

Brief sign, accepted with time, by Mary (9)
MOMENTARY — OMEN (sign) T (time) inside MARY

13

Teams reject passing criticism (9)
SIDESWIPE — SIDES (teams) WIPE (reject)

16

Be impressed with new term for fanatic (9)
EXTREMIST — EXIST (be) containing anagram (new) of TERM

17

Head of school studied hard and left quickly (8)
SCRAMMED — S (head of school) CRAMMED (studied hard)

20

Gold rush on the north side of a US state capital (7)
AUGUSTA — AU (gold) GUST (rush) A

22

One who may throw out event's first champion (7)
EVICTOR — E (first letter of event) VICTOR (champion)

23

At home with duets arranged by leader of orchestra (4,2)
USED TO — anagram (arranged) of DUETS, O (first letter of orchestra)

25

Large section of church could be falling away (5)
LAPSE — L (large) APSE (section of church)

27

Live on banks of river, next to a hillside (4)
BRAE — BE (live) containing R (river) A