Will linking a third party router affect bt sport
It depends how you watch BT Sport.
If it's via a Youview box then whatever replacement you get has to fully support Multicast transmission and IGMP Snooping.
If it's via the app I can't see that it matters.
When you say "linking" do you mean replacing the BT Smarthub with a third party router or do you mean including the third party router along with your BT Smarthub as an additional router or wireless access point?