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Knock off Rockefeller's emerald? (3)

https://emeralds.com/education/rockefeller-emerald/

No new decent diamonds (3)

Chip first to eat dessert (3)

Kill for diamonds (3)

In case of emergency initially apply to reduce swelling (3)

Glacé in Nice, non? Oui! (3)

NICE - N
NON = NO “N”

Glacé is French for ice., also an inclusion.
Trying to be too clever perhaps

Reserve some juice (3)

Ancient drug (3)

ICE = 1 CE ( common era)

Freeze kicker at prime times (3)

American football reference. To "freeze (or ice) the kicker" is to call a timeout just before a crucial kick, presumably to give the kicker time to think about it and get nervous. It rarely works but coaches do it anyway. (Positions 2, 3, 5 in "kicker".)

Soft serve from No.1 indicates stiffness (3)

Soft serve - ice (cream) No.1 - top seed/ranked player
Stiffness (def.)- coldness of manner

Well, it is Wimbledon...