KlingonMusic.Net has a list of references to Klingon music in Star Trek episodes. The entries specifically identified as Klingon Opera, and which involved some on-screen representation (as opposed to characters just talking about it) are:
- The example in your question:
‘aqtu’ mellota’ je – Klingon Opera, excerpt sung by Worf and Amarie in
TNG: “Unification II” (“Aktuh and Maylota” in script; “Aktuh and
Melota” in TKW)
- A separate piece used in two Deep Space Nine episodes:
“BOOOOW-cha-daaay” – a duet from a Klingon Opera (referred to as a
“Klingon La Boheme” in the script) that Worf sings (and acts) along
with in the Defiant during DS9: “Looking For par’Mach in All the Wrong
Places;” a shorter excerpt from the same opera is heard in the episode
of DS9: “In The Cards” while Nog is filtering out subharmonic
frequencies in Worf’s Klingon Opera collection.
Other entries from the list which were actually sung in episodes are just Klingon "songs" rather than opera per se, but they may also be of interest.