TL;DR: T-cells are primarily responsible for both acute (weeks to months) and chronic (months to years) rejection; this would be acute rejection [FA2020 p119]

Hyperacute rejection (minutes): from pre-formed antibodies in the recipient which trigger an immune response in the recipient via complement activation (Type II hypersensitivity)

Acute Rejection (weeks to months): recipient T-cells recognize donor MHC on donor dendritic cells (Type IV hypersensitivity); humoral component (Type II hypersensitivity) to a lesser extent AFTER the T-cells have recognized the MHC as foreign

Chronic (months to years): recipitent T-cells recognize alloantigens [which are antigens which would be self in a normal tissue in the donor, but are recognized as foreign in the recipient] presented by recipient dendritic cells (Type IV hypersensitivity); humoral component (Type II hypersensitivity) AFTER the T-cells have recognize the MHC as foreign