People initially relish good service (4)
I believe the answer is:
race
'people' is the definition.
(people can mean a national group or race)
'initially relish good service' is the wordplay.
'initially' says to take the initial letters.
'good service' becomes 'ace' (a good serve in tennis).
The initial letter of 'relish' is 'r'.
'r'+'ace'='RACE'
(Other definitions for race that I've seen before include "People; run" , "Career - people" , "Run fast" , "eg The Oaks" , "People - sprint - competition" .)