I see no need to move him. We have a lot of bodies, but not a quality depth chart on D.
Brannstrom's development reminds me a lot of Ryan Ellis. Brannstrom turned pro quicker, but both played their first two years after being drafted outside the NHL, and then were part-time AHL/NHL for two years, before settling in a relatively regular NHLers. The improvement tends to really start around now, which we have seen signs of this year.
Both players are undersized offence-first guys, but both have decent frames. Ellis might be a bit naturally better in the defensize zone, but he really grew into that. I'd say Brannstrom is quite a bit better skater. So just like Ellis in Nashville, Brannstrom could play a key role even if he doesn't become a #1 D. He can also really run a PP, as we have seen with Chabot out. This is good insurance for when Chabot goes down, or even just PP2.