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' says to take the centre.
The middle letters of 'kept' are 'ep'.
'we'+'ep'='WEEP'
'to' is the link.
(Other definitions for weep that I've seen before include "Express grief or sorrow" , "lament" , "pipe" , "Turn on the waterworks" , "Sob - ooze" .)