Old boy has a couple of teeth to eat fish that's out of date (8)
I believe the answer is:
obsolete
'out of date' is the definition.
(I've seen this before)
'old boy has a couple of teeth to eat fish' is the wordplay.
'old boy' becomes 'ob' (abbreviation).
'has' means one lot of letters go next to another.
'a couple of teeth' becomes 'et' (I can't explain this - if you can you should believe this answer much more).
'to eat' indicates putting letters inside (word on the right has word on the left to eat).
'fish' becomes 'sole' (sole is a kind of fish).
'et' put within 'sole' is 'solete'.
'ob'+'solete'='OBSOLETE'
'that's' acts as a link.
(Other definitions for obsolete that I've seen before include "'No longer used, out of date (8)'" , "Dead" , "No longer current" , "Outdated" , "Boots eel away, being out of date" .)