Yes, they can regenerate
Tarantulas can regrow lost limbs over subsequent moults. The first replacement may be smaller or thinner than the original and can become more normal over later moults.
Young spiders recover faster
Slings and juveniles moult more often, so regeneration can progress more quickly than in an adult female that may wait a long time between moults.
The immediate injury matters
A missing leg is less urgent than uncontrolled haemolymph loss. If an injury is actively leaking or the spider is collapsing, seek specialist veterinary advice.
Make access easy
Keep the enclosure simple and ensure the spider can reach water without climbing or struggling. Avoid unnecessary rehousing while the animal adapts.
Do not force extra feeding
More food does not magically accelerate regeneration. Feed normally according to body condition and allow the spider's own moult cycle to do the work.
Future moults
Record the injury and subsequent moults. Seeing the regenerated limb develop across stages is useful for monitoring recovery without repeatedly disturbing the spider.