Complaint with half the Te Deum being played on a pipe (6)
I believe the answer is:
fluted
'being played on a pipe' is the definition.
'complaint with half the te deum' is the wordplay.
'complaint' becomes 'flu' (flu is a kind of health problem).
'with' means one lot of letters go next to another.
'half the' means to take half the letters.
'deum' becomes 'ed' (I can't justify this - if you can you should believe this answer much more).
'te' cut in half is 't'.
'flu'+'t'+'ed'='FLUTED'
(Other definitions for fluted that I've seen before include "Grooved" , "Ornamented with grooves" , "Groovy?" .)