More convenient, that is, with Chinese doctor coming round (7)
I believe the answer is:
handier
'more convenient' is the definition.
('handy' can be similar in meaning to 'convenient')
'that is with chinese doctor coming round' is the wordplay.
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'with' says to put letters next to each other.
'chinese' becomes 'han' (Chinese dynasty).
'doctor' becomes 'dr' (abbreviation).
'coming round' means one lot of letters goes inside another.
'han' next to 'dr' is 'handr'.
'ie' inserted inside 'handr' is 'HANDIER'.
(Another definition for handier that I've seen is " More convenient".)