Possible Clues:

• Small tropical American monkey
• Indianapolis indie band named after a New World monkey
• Brought into market there's some strange monkey
• Encountered, traversing branch, very big monkey
• Monkey, hurt, doctor located
• Tamarin relative
• Spoil the doctor's alien monkey
• Little monkey's limb held by medic to repair break
• Rodent wanting tail fixed finds monkey
• Animal doctor the new master brought in