Suffer having to change rig with first mate (6)
I believe the answer is:
grieve
'suffer' is the definition.
(grieving is a kind of suffering)
'to change rig with first mate' is the wordplay.
'to change' indicates anagramming the letters.
'with' is a charade indicator (letters next to each other).
'first mate' becomes 'eve' (I've seen this before).
'rig' is an anagram of 'gri'.
'gri'+'eve'='GRIEVE'
'having' is the link.
(Other definitions for grieve that I've seen before include "Feel intense sorrow at someone's death" , "Cause great distress to" , "Mourn, feel sorrow" , "Mourn, lament" , "Mourn loss" .)