Can't expect to much since maybe this year will be different and but I'm speculating that maybe we can't see those bullish season which bitcoin goes pump as hard as before. Maybe we can see this season when halving nearly came nor take effect in future since this is mostly one big event which make bitcoin pump more higher. Maybe the best one to speculate is what will be the price reached on next halving.
If you are talking about Bitcoin rallies towards breaking ATH, I think we had observed it before. It somehow starts some months before the Bitcoin halving. Probably because of the lesser Bitcoin influx hype, then the market calms down (going sideways) for a few months after the halving. Then start to surge again towards ATH breaking rallies. This cycle never fails to happen during those Bitcoin halving events. So yeah, I think history will repeat itself.