Shine, having first to break depression (7)
I believe the answer is:
glisten
'shine' is the definition.
('glisten' can be a synonym of 'shine')
'first to break depression' is the wordplay.
'first' becomes 'ist'.
'to break' means one lot of letters goes inside another.
'depression' becomes 'glen' (glen is a kind of depression**).
'ist' placed into 'glen' is 'GLISTEN'.
'having' is the link.
(Other definitions for glisten that I've seen before include "'Shine, as if wet (7)'" , "Shine or sparkle wetly" , "Singlet (anag.); tingles (anag.)" , "Shine with reflected light" , "Be a shining example" .)