Golfers can only carry a limited number of golf clubs in their bag for a single round of golf. They can't carry however many golf clubs as they want.
Under the Rules of Golf, a golfer is only allowed to carry 14 clubs in their bag. The makeup of that bag can be whatever the golfer wants, so long as the clubs are conforming under the rules of the U.S. Golf Association and/or the R&A. A golfer doesn't have to carry a driver, a putter or any other club, so long as they add up to 14 or less.
If a golfer carries more than 14 clubs in their golf bag, they're breaking the Rules of Golf -- specifically, Rule 4. In tournament competition, the maximum penalty for carrying too many golfs clubs is four shots. A player is penalized two strokes per hole with an extra club in the bag, up to four strokes. In match play, the maximum penalty is a loss of hole per each hole with more than 14 clubs in the bag, up to two holes lost.
If a golfer starts a round of golf with less than 14 clubs, then can add clubs to their bag during the round until they have 14 clubs. Those clubs cannot be borrowed from another player, even if they're on the golfer's team in a match situation.
Golfers are also not allowed to change golf clubs during the round under most circumstances. That means a golfer has to finish a round of golf with the same 14 clubs with which they began the round unless the club is damaged in the normal course of play.
Once a new round begins (including a playoff in a stroke-play competition), a player can swap out clubs and have a new bag of 14 for the start of a new round.
The 14-club limit was proposed by the USGA in 1938 and adopted by the R&A in 1939. Before then, golfers had in upwards of 20 or 25 clubs in their bags to get through a round using equipment that had hickory shafts, susceptible to breaking.