Get to know tragic character close to queen (5)
I believe the answer is:
learn
'get to know' is the definition.
(synonyms)
'tragic character close to queen' is the wordplay.
'tragic character' becomes 'lear' (I've seen this before).
'close to' suggests the final letters (the 'close' to the word).
The last letter of 'queen' is 'n'.
'lear'+'n'='LEARN'
(Other definitions for learn that I've seen before include "Ascertain" , "Read up on" , "Take in" , "teach illiterate" , "Study - find out" .)