Yours is a "wide open" question.
Obviously, you have a barrel with a .308 bore. Going to a larger caliber would mean cutting out and re rifling, rule of thumb, at least 2 calibers larger minimum(per mr. Ackley), so anything .32 up... within barrel limit.
Smaller means relining/rechambering. About anything is possible there too.
BRING MONEY. lots and lots. It will not be cheap.
Quick, simple, cheapest (but not cheap), you have an extractor set up for the standard mauser rim, approx. .473 and used on the .308 WCF. Anything else, simple, is a possible "longer" chamber. .30/'06 is probably first in line. .35 Whelan would mean a rebore/rechamber...
From there you come to the question of the action's capacity for pressure. .308 Works at the 55K CUP standard on its rim. If you choose to rechamber to a larger diameter case--a belted case, then you spread more pressure over the rim area. Too much? Good question. You could check with the factory or just look at calibers available. I don't think .300 H&H or WCf will be on the list, but possible. Not smart, but possible.
Cheaper way is to buy another, interchangeable barrel. As a rule factory tolerances are a bit sloppy and you can improve accuracy if you or a gunsmith "fits" that barrel to your action. MUCH CHEAPER. But it is your project. Your bucks, your call. luck.
The 7 TCU is a 7mm (.284) bullet in the .223 case. The .223 is a .224 bullet. Standard twists, 7mm uses bullets in the 100 grain to 190 grain range. Out of the .223 case, power adequate for deer at closer ranges. The idea was to keep kick down for the handgun shooter. .223 uses bullets in the 35 grain to 80 grain range or so and is questionable on deer in general use. What do you want? A deer rifle? A varmint rifle? Both?
I think it would be cheapest, if available, to buy a 7mm Waters barrel if you want a 7mm deer rifle. If you are thinking varmints, then .223 is very popular. You could, AT GREAT EXPENSE, reline/rechamber your .308 barrel to these calibers, but there are many things I would rather spend money on. again, your call, luck