WHAT'S HAPPENING IN PARLIAMENT THIS WEEK?

* Speaker Tony Smith to issue writ on Monday for October 20 by-election in NSW seat of Wentworth, vacated by Malcolm Turnbull.

* Labor to pursue Home Affairs Minister Peter Dutton over his eligibility for parliament, but is awaiting coalition MP backing.

* Senate inquiry report due on Wednesday into Dutton's use of ministerial powers in relation to au pairs.

* Greens may seek parliamentary support for no confidence motion in Dutton.

* Inquiry report due on Tuesday into the Trans-Pacific Partnership trade pact.

* Senate committee to report on Wednesday into the future of work and the "gig" economy.

* Senate to debate laws to crack down on tax avoidance, and a bill to ensure the ABC is "fair and balanced" and better covers rural and regional audiences.

* Senate to consider Labor bill expanding the Productivity Commission's functions to include researching inequality.

* Inquiry hearing on Tuesday into the controversial granting of $444 million to the Great Barrier Reef Foundation.

* Aged care standards expected to be key issue, following weekend announcement of a royal commission.

* Labor caucus and coalition joint party room to meet on Tuesday.