Moffat almost killed himself with introducing Smith, 2 companions and the coming of a whole new era with the 11th Hour, but even then he still had little links like Murray Gold and the general structure of his first season (Plus the fact he had written some of if not the best episodes of NeWho up to that point). Then with Capaldi he had both Clara and previous characters he had created to work with, plus a lot less to have to actually do (Only really introduce a new Doctor).
Moffat also had River Song to connect seasons 4 and 5.
This is another thing that bothered me about Spyfall—why did they need to create a brand new British intelligence agency when the show's history provided so many to choose from?
And, could they not get either Missy or the RTD-era guy to play The Master? I liked Agent Oh, but it would have been the perfect opportunity to bring back a familiar face.
They needn't go massively out of there way to cater to old viewers, but it'd be nice if they threw us a bone or two, just to acknowledge that the past actually happened.