Dines out after a turn, having worried greatly (8)
I believe the answer is:
agonised
'worried greatly' is the definition.
(I've seen this before)
'dines out after a turn' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'after' is a charade indicator (letters next to each other).
'turn' becomes 'go' (a person's move in a board game**).
'dines' with letters rearranged gives 'nised'.
'a'+'go'='ago'
'nised' after 'ago' is 'AGONISED'.
'having' is the link.
(Other definitions for agonised that I've seen before include "Felt mental anguish (over a decision)" , "San Diego (anagram)" , "Suffered mentally in San Diego" , "Dog in sea (anag) - suffered anguish" , "Very pained" .)