Glimpse face of duke, a court favourite (4)
I believe the answer is:
seed
'a court favourite' is the definition.
(highly rated player on a tennis court)
'glimpse face of duke' is the wordplay.
'glimpse' becomes 'see' (I've seen this before).
'face of' indicates taking the first letters.
The first letter of 'duke' is 'd'.
'see'+'d'='SEED'
(Other definitions for seed that I've seen before include "From which things grow" , "Court favourite" , "Kernel" , "- Pearl; - capital" , "Pip for sowing" .)