Low Earth Orbit (LEO) satellite networks have revolutionized space internet access, offering better network performance than previous alternatives. While being the best option for space internet access, it does not yet compete with terrestrial networks in latency and bandwidth. The QUIC transport protocol was developed for Hypertext Transfer Protocol (HTTP) to reduce page load times and work better in low-bandwidth and high-loss networks than the Transmission Control Protocol (TCP). Studies have shown that QUIC performs well for small file sizes, which can be achieved by using compression. This thesis investigates whether combining QUIC as a general data transfer protocol with lossless compression enhances encrypted data transmission in a LEO satellite network. To test this, a program consisting of a client and server deployed on a LEO satellite network emulator is developed, where files with increasing sizes are compressed and sent using both QUIC and TCP in various network conditions. Results indicate that QUIC should be paired with lossless compression for file sizes up to 1MB. It should not be implemented for file sizes above 1MB in low-loss and high-bandwidth conditions, while it can be implemented in medium to poor conditions.