Good time in bowls game promised (7)
I believe the answer is:
engaged
'promised' is the definition.
(synonyms)
'good time in bowls' is the wordplay.
'good' becomes 'g' (abbreviation).
'time' becomes 'age' (an age is a period of time).
'in' is an insertion indicator.
'bowls' becomes 'end' (I can't justify this - if you can you should believe this answer much more).
'g'+'age'='gage'
'gage' inserted within 'end' is 'ENGAGED'.
'game' acts as a link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for engaged that I've seen before include "preparing for the match?" , "Affianced" , "Occupied with business - about to marry?" , "Plighted; hired" , "May as well ring off" .)