Solution to 1D has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to solve, if not solved by 1 PM.
ACROSS
7 Probe worker posing as influencer (5,6) POWER BROKER*
8 Beauty spot basically in skin, perhaps acne (3) SPA Acrostic
10 Took advantages of cues read periodically (4) USED {cUeS+rEaD}
11 GATE, NEET or IIT-JEE’s portions (5) TORII [T]
12 Circulating attaché’s proposal (4) IDEA (-a)IDE(+a)A
13 Tiny part appeared ordinary (5) CAMEO {CAME}{O}
15 Spooner’s chief gardener’s a valuable employee (9) RAINMAKER (~main raker to rainmaker)
16 Small crew controls royal jet (6) STREAM {S}{T{R}EAM}
21 Dead jail bird tipped to smuggle drugs at first (9) CONCLUDED {CON}{CLU{Dr..s}ED}
23 Oddly selected UK guards in new year (5) UGADI {Uk+GuArDs+In}
25 Prejudice in British civil service (4) BIAS {B}{IAS}
26 Jerk tackles work subject (5) TOPIC {T{OP}IC}
27 Colony resident hosting posh relative (4) AUNT {A{U}NT}
28 Embarrassed in fling (3) SHY [DD]
29 Stymie attack behind Putin (3,2,3,3) NIP IN THE BUD*
DOWN
1 Fixed fan during study time (8) ?O?S?A?T (Addendum - CONSTANT {CON}{STAN}{T} - See comments)
2 Initially found enemies using daggers in rivalry (4) FEUD Acrostic
3 Sailor had to sink (5) ABATE {AB}{ATE}
4 Diary of sweetheart, a student smoking pot (7) JOURNAL {JO}{URN}{A}{L}
5 Gave up degree for writing as planned (8) DESIGNED (-r+d)DESIGNED
6 Non-commercial tool covering that woman's domain (6) SPHERE {SPad{HER}E}
9 Encounter a problem against husband at work (3,1,4) HIT A SNAG {AGAINST+H}*
14 Training in duty overcoming hesitation (8) EXERCISE {EX{ER}CISE}
17 Sex change at the onset of spring makes one peak (8) MOUNTAIN (-f+m)MOUNTAIN
19 Player Liren entertained by joke about finishing (6,2) ENDING UP {E}{N{DING}UP<=}
20 Paradise lost without a hope? Just the opposite! (7) DESPAIR PARaDISE*
24 Critical crop planted in area regularly (5) ACUTE {Ar{CUT}Ea}
27 Cross monkey climbing above top (4) APEX {X}<=>{APE}
Reference List
Ordinary = O, Small = S. Royal = R, British = B, Posh = U, Time = T, Sailor = AB, Sweetheart = JO, Studdent = L, Degree = D, Writing = R, Commercial = AD, Husband = H, Player = E