Is it possible to obtain RefSeq transcripts from Ensembl database for GRCh37 to match Ensembl Genes?
The RefSeq match option in BioMart is from the Matched Annotation from NCBI and EBI (MANE) collaboration between RefSeq and Ensembl. It has only been calculated for the up-to-date gene annotation on GRCh38 so cannot be obtained on GRCh37. You can get mapping from Ensembl to RefSeq transcripts through BioMart as RefSeq mRNA ID (refseq_mrna in R) but this is not a perfect match like the MANE, it is a mapping based on sequence similarity and similar genomic location, and there can be mismatches between them.