You must find Infernal Iron and take it to Dammon the blacksmith (found at the Emerald Grove or Last Light Inn) to repair her heart.

Karlach's romance is a "slow burn" defined by her heart, which prevents physical touch until she is repaired. How to Romance:

Note: Though the user wrote "Carla," this is the most common modern search intent.

Carla ’s romantic arc in Elite revolves around power, manipulation, and eventually, a search for genuine connection. Carla Rosón Caleruega - Elite Wiki | Fandom

Because "Carla" is a central character in several major franchises, this guide covers the romantic storylines for the three most prominent versions of the character. Karlach (Baldur's Gate 3)

Recruit her on the Risen Road . Earn high approval by being kind, helping innocents, and being decisive with enemies.