Oscar and Elizabeth taking in small hound (6)
I believe the answer is:
obsess
'hound' is the definition.
'oscar and elizabeth taking in small' is the wordplay.
'oscar' becomes 'o' (phonetic alphabet: alpha, bravo, charlie etc.).
'and' says to put letters next to each other.
'elizabeth' becomes 'bess'.
'taking in' means one lot of letters goes inside another.
'small' becomes 's' (abbreviation - e.g. clothes size).
'bess' going around 's' is 'bsess'.
'o'+'bsess'='OBSESS'
(Other definitions for obsess that I've seen before include "Bosses (anag.)" , "Preoccupy completely" , "Prey on" , "Persistently preoccupy" , "Plague" .)