I'll stick around to get a soothing lozenge (8)
I believe the answer is:
pastille
'a soothing lozenge' is the definition.
'pastille' can be an answer for 'lozenge' (pastille is a kind of lozenge). I'm not certain of the 'a soothing' bit.
'i'll stick around' is the wordplay.
'stick' becomes 'paste' (I've seen this in another clue).
'around' means one lot of letters goes inside another.
'ill' going inside 'paste' is 'PASTILLE'.
'to get' is the link.
Can you help me to learn more?
(Other definitions for pastille that I've seen before include "something for a sore throat" , "Cough lozenge" , "Lozenge, small sweet for sucking" , "Small sweet/lozenge" , "One medicated sweet is the alternative" .)