No
The stat block for a tiger lists these actions:
Actions
Bite. Melee Weapon Attack: +5 to hit, reach 5 ft., one target. Hit: 8 (1d10 + 3) >piercing damage.
Claw. Melee Weapon Attack: +5 to hit, reach 5 ft., one target. Hit: 7 (1d8 + 3) slashing damage.
Compare this to the stat block of a polar bear:
Actions
Multiattack. The bear makes two attacks: one with its bite and one with its claws.
Bite. Melee Weapon Attack: +7 to hit, reach 5 ft., one target. Hit: 9 (1d8 + 5) >piercing damage.
Claws. Melee Weapon Attack: +7 to hit, reach 5 ft., one target. Hit: 12 (2d6 + 5) slashing damage.
The tiger stat block lacks the multiattack option which would allow both a claw and a bite attack. They could normally only use both during the same turn if they moved at least 20 feet towards their target, then made a successful claw attack and had the target fail their save, before using making the bite attack as a bonus action. Aside from that it would require some special effect like the haste spell to allow it.