TG stans and this fantasy that they themselves created that the house hightower has relevance in the asoiaf universe, let's be honest, the dance was the only moment they had their 10 minutes of fame lol yes! they are a good house (loyal to house targaryen currently) but they are not relevant afterwards... they are not on the level of targaryens, tyrells, baratheon, starks etc hightowers have no impact on the books currently, even the Greyjoys are more relevant lol
TG stans must hate the ASOIAF timeline so much lmao. House Hightower's only actions have been through Ser Gerold, who was the lord commander of Aerys' Kingsguard. The head of the house, Lord Leyton has locked himself in a tower and is suspected of experimenting with magic, in direct conflict with the Faith and the Citadel.
After the Dance, the Hightowers are only ever seen either keeping to themselves or supporting the Targaryens. In the Blackfyre rebellion, they officially supported neither camp, that's the only somewhat exception.
I've seen some of them wave around Rhaena's marriage to Gormund Hightower as if that's some kind of victory, when really it just cements House Hightower's renewed allegiance to the Targaryens.
The Hightowers have very little significance after the Dance. Their power in terms of the realm is equal to houses like the Freys and the Boltons, but they do so much less than both of them. Their ties to the Fatih and the Citadel are their claims to power, and Leyton is possibly damaging those.
Honestly I think they will come into play in TWOW, what with the ironborn invasion and Leyton's interest in magic. However, they will not take center stage nor be as significant as they were in the Dance. That was their moment of greatest political power, and they won't return to that.