Stick with a brood including son (7)
I believe the answer is:
persist
'stick with' is the definition.
(I've seen this before)
'a brood including son' is the wordplay.
'a' becomes 'per'.
'brood' becomes 'sit' (I've seen this before).
'including' means one lot of letters goes inside another.
'son' becomes 's'.
'sit' enclosing 's' is 'sist'.
'per'+'sist'='PERSIST'
(Other definitions for persist that I've seen before include "Keep going" , "Pursue course doggedly" , "Continue firmly or obstinately" , "Endure" , "Continue to exist" .)