Be given thanks by letter (4)
I believe the answer is:
beta
'letter' is the definition.
(beta is a kind of letter)
'be given thanks' is the wordplay.
'given' is a charade indicator (letters next to each other).
'thanks' becomes 'ta' (UK informal version of 'thank you').
'be'+'ta'='BETA'
'by' acts as a link.
(Other definitions for beta that I've seen before include "Second Greek letter, B" , "Character between alpha and gamma" , "2nd letter of Greek alphabet" , "Second Greek letter - beat that" , "testing stage" .)