I know this is a massive ‘what if’ but if British Aerospace had won the contract for the JSF with the Harrier GR11 what would the aircraft look like?

By “contract for the JSF” you mean British Aerospace being the prime contractor and winning the Pentagon competition for the USAF/US Navy/Marine Corps replacement for 7/10 of the entire american tatical fast jet fleet?
Thats not a massive “what if”, thats pretty much impossible.

The GR7/9 have many general design similarities with the GR1/3 but are clearly much more advanced designs, how would 21st century engineering, aerodynamics and avionics have been incorporated in to the Harrier GR11?

You could throw every ” 21st century engineering, aerodynamics and avionics ” into the Harrier airframe that it still wouldnt be capable of cover one single KPP for the JSF program except “getting airborne”. 😀

If your question is “what would a new ASTVOL BAE design after the Harrier look like”, well, like this:

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Cheers