Brilliant squeezing new spots (4)
I believe the answer is:
acne
'spots' is the definition.
(skin condition causing spots)
'brilliant squeezing new' is the wordplay.
'brilliant' becomes 'ace' (I've seen this before).
'squeezing' is an insertion indicator (squeeze can mean hug or embrace).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'ace' placed around 'n' is 'ACNE'.
(Other definitions for acne that I've seen before include "Inflammation of glands in skin" , "Pimply ailment of adolescnce" , "Spotty coverage" , "sort of disease" , "Skin complaint" .)