Glum without my round old English dog (7)
I believe the answer is:
samoyed
'dog' is the definition.
(Samoyed is an example)
'glum without my round old english' is the wordplay.
'glum' becomes 'sad' (I've seen this in another clue).
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'round' means one lot of letters goes inside another.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'english' becomes 'e' (abbreviation).
'my' going around 'o' is 'moy'.
'moy'+'e'='moye'
'sad' placed around 'moye' is 'SAMOYED'.
(Other definitions for samoyed that I've seen before include "Siberian dog" , "not setter!" , "one barking" , "Some day (anag) - dog (from Siberia?)" , "Sled dog" .)