ABSTRACT We report observations of the highly active FRB 20240114A with MeerKAT using the ultra-high frequency (UHF; $544\!-\!1088$ MHz) and L band ($856\!-\!1712$ MHz) receivers. A total of 62 bursts were detected in coherent tied-array beams using the MeerTRAP real-time transient detection pipeline. We measure a structure-optimizing dispersion measure of $527.65\pm 0.01\, \text{pc}\, \text{cm}^{-3}$ using the brightest burst in the sample. We find the bursts of FRB 20240114A are generally detected in part of the broad-band of MeerKAT, $\sim 40~{{\ \rm per\ cent}}$ in the UHF and $\sim 30~{{\ \rm per\ cent}}$ in the L band, indicating the band limited nature. We analyse the fluence distribution of the 44 bursts detected at UHF, constraining the fluence completeness limit to $\sim 1$ Jy ms, above which the cumulative burst rate follows a power law $R (\gt F)\propto (F/1\, \text{Jy}\, \text{ms})^\gamma$ with $\gamma =-1.8\pm 0.2$. Using channelized telescope data captured in our transient buffer we localize FRB 20240114A in the image domain to RA = 21h27m39.86s, Dec. = +04d19m45.01s with an uncertainty of 1.4 arcsec. This localization allows us to confidently identify the host galaxy of FRB 20240114A. Also using the transient buffer data, we perform a polarimetric study and demonstrate that most of the bursts have $\sim 100~{{\ \rm per\ cent}}$ linear polarization fractions and up to $\sim 20~{{\ \rm per\ cent}}$ circular polarization fractions. Finally, we predict the flux density of a potential persistent radio source (PRS) associated with FRB 20240114A is $\backsimeq [0.6\!-\!60]\, \mu \text{Jy}$ based on the simple relation between the luminosity of the PRS and the rotation measure arising from the FRB local environment.
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