Artist in Baltic state given thanks for opera (2,8)
I believe the answer is:
la traviata
'opera' is the definition.
(Verdi opera)
'artist in baltic state given thanks' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'in' means one lot of letters goes inside another.
'baltic state' becomes 'latvia' (one of the three Baltic countries).
'given' means one lot of letters go next to another.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'ra' going inside 'latvia' is 'latravia'.
'latravia'+'ta'='LA TRAVIATA'
'for' is the link.
(Other definitions for la traviata that I've seen before include "work" , "Verdi opera" , "Verdi's Dumas opera" .)