Unlimited time to append a few words to biography (4,8)
I believe the answer is:
life sentence
'unlimited time' is the definition.
'words to biography' is the wordplay.
'words' becomes 'sentence' (I've seen this before).
'to' means one lot of letters go next to another (I've seen this in other clues).
'biography' becomes 'life' (synonyms).
'sentence' put after 'life' is 'LIFE SENTENCE'.
'to append a few' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
(Other definitions for life sentence that I've seen before include "Long prison stay" , "Long punishment" , "Maximum stretch?" , "Long-term punishment" , "short extract from American magazine" .)