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We report 4 new pulsars discovered in the core-collapsed globular cluster (GC) NGC 6624 by the TRAPUM Large Survey Project with the MeerKAT telescope. All of the new pulsars found are isolated. PSR J1823$-$3021I and PSR J1823$-$3021K are millisecond pulsars with period of respectively 4.319 ms and 2.768 ms. PSR J1823$-$3021J is mildly recycled with a period of 20.899 ms, and PSR J1823$-$3022 is a long period pulsar with a period of 2.497 s. The pulsars J1823$-$3021I, J1823$-$3021J, and J1823$-$3021K have position and dispersion measure (DM) compatible with being members of the GC and are therefore associated with NGC 6624. Pulsar J1823$-$3022 is the only pulsar bright enough to be re-detected in archival observations of the cluster. This allowed the determination of a timing solution that spans over two decades. It is not possible at the moment to claim the association of pulsar J1823$-$3022 with the GC given the long period and large offset in position ($\sim 3$ arcminutes) and DM (with a fractional difference of 11 percent compared the average of the pulsars in NGC 6624). The discoveries made use of the beamforming capability of the TRAPUM backend to generate multiple beams in the same field of view which allows sensitive searches to be performed over a few half-light radii from the cluster center and can simultaneously localise the discoveries. The discoveries reflect the properties expected for pulsars in core-collapsed GCs.