How does repair take place on leading strand in eukaryotes?
I'll keep the answer to this as concise as possible. The major mismatch repair (MMR) pathway used by eukaryotes is the MutS$\alpha$-MutL$\alpha$-dependent MMR. See the diagram below for its mechanism:



The pathway initiates when MutS$\alpha$ (Msh2–Msh6) binds to a mismatch. This is followed by binding of MutL$\alpha$ (Mlh1 and Pms2). PCNA then activates MutL$\alpha$ to incise the nascent strand and the DNA ends are used for removing the replication error. After this, the repair is completed by correct DNA synthesis and ligation (note that this pathway works in both leading and lagging strands). DNA replication and MMR are temporally coupled in a manner that may be related to the regulation or appearance of the signals used for MMR. Also, pay attention to the point that the opposite strand is used as reference strand for repair and the strand to which MutL$\alpha$ binds is the one at which Pol$\epsilon$ (or Pol$\delta$) replicates as the DNA polymerase and the PCNA act as the signal for MutL$\alpha$ activity.

See this paper (also the image source) by Kunkel and Erie (2015), they describe this process and a lot of things related to it, including its regulation and signals, in much more detail. I haven't talked much about the details here as the paper is a much better source to understand them.

References:


Kunkel TA, Erie DA. Eukaryotic Mismatch Repair in Relation to DNA Replication. Annu Rev Genet. 2015;49:291–313. doi:10.1146/annurev-genet-112414-054722