best option is to run some external grade ethernet cable (cat5e or better) from the hub to the outbuilding.. if the outbuilding has power, then you can buy something like this to broadcast a wifi signal down there..
if there is no power in the summerhouse then you could use something like this which can be powered via the ethernet cable (this model includes a PoE injector which you'd have to connect in the house..)
I started with a pair of wifi bridges. But was only getting about 750Mb. So suspended a pair of cat5e off a catenary wire and with link aggregation got a solid 1 Gb at any device irrespective of what traffic was crossing. I shift a lot of large files.
Since then I have replaced the cat 5 with fibre. Although only using 1 pair to give a 10Gb connection to the garden room there is a second pair available.,
Speed was not the only incentive. Several years ago. My parents who live in a glacial valley have their TV arial on top of a telegraph pole on top of a large bank. So about 100ft above house height got a lighting strike. It took out everything connected. 4 tvs, videos, hifi system and destroyed a ringmain blowing breakers requiring a rewire. Fortunately the insurance paid.i therefore decided the 50ft of cat5 with multiple earths dangling across the lawns too big a target. so fibre.
If your power is from the same circuit as the house ring main then if you just wanted to browse internet etc the simplest option would be to use something like TP powerline. For more advanced use then run cat5e cable as described above by tehwolf