We kept inside to grieve (4)
I believe the answer is:
weep
'grieve' is the definition.
(I've seen this in another clue)
'we kept inside' is the wordplay.
'inside' indicates the central letters.
The middle of 'kept' is 'ep'.
'we'+'ep'='WEEP'
'to' acts as a link.
(Other definitions for weep that I've seen before include "Express grief or sorrow" , "lament" , "pipe" , "Turn on the waterworks" , "Sob - ooze" .)