The Large Magellanic Cloud (LMC) presents a unique environment for pulsar population studies due to its distinct star formation characteristics and proximity to the Milky Way. As part of the TRAPUM (TRAnsients and PUlsars with MeerKAT) Large Survey Project, we are using the core array of the MeerKAT radio telescope (MeerKAT) to conduct a targeted search of the LMC for radio pulsars at L-band frequencies, 856–1712 MHz. The excellent sensitivity of MeerKAT, coupled with a 2-hour integration time, makes the survey 3 times more sensitive than previous LMC radio pulsar surveys. We report the results from the initial four survey pointings which has resulted in the discovery of seven new radio pulsars, increasing the LMC radio pulsar population by 30 per cent. The pulse periods of these new pulsars range from 278 to 1690 ms, and the highest dispersion measure is 254.20 pc cm−3. We searched for, but did not find any significant pulsed radio emission in a beam centred on the SN 1987A remnant, establishing an upper limit of 6.3 μJy on its minimum flux density at 1400 MHz.