Is it permissible for an agent to keep a portion of zakat funds paid to relatives to contribute to a future, unspecified surgery for one of them, and how should these retained funds be handled?

There is no harm in giving zakat (definition) to a poor relative who cannot afford the cost of treatment or surgery, or who is in debt, as this is considered one of the categories for zakat expenditure. However, it is not permissible to delay zakat beyond its due time, except for a short period for a benefit or a need.