Impulsively hosting King and I with a certain charm (8)
I believe the answer is:
rakishly
'with a certain charm' is the definition.
(with a rakish charm)
'impulsively hosting king and i' is the wordplay.
'impulsively' becomes 'rashly' (rash can mean impulsive or thoughtless).
'hosting' is an insertion indicator (inserted letters are welcomed in or hosted).
'king' becomes 'K' (abbreviation for king in chess).
'and' means one lot of letters go next to another.
'k'+'i'='ki'
'rashly' placed around 'ki' is 'RAKISHLY'.
(Other definitions for rakishly that I've seen before include "jauntily" , "jaunty fashion" , "aslant" .)