Is it possible to obtain RefSeq transcripts from Ensembl database for GRCh37 to match Ensembl Genes? I know that with GRCh38, it is possible to extract the matching RefSeq transcripts for Ensembl genes/transcripts/proteins using Biomart from Ensembl. 

However, for GRCh37, this option does not exists. Using the following MySQL command returns Ensembl transcript IDs for matching RefSeq transcripts:

mysql -u anonymous -h ensembldb.ensembl.org -A -P 3337 -D homo_sapiens_core_99_37 -e "SELECT transcript.stable_id, xref.display_label FROM transcript, object_xref, xref,external_db WHERE transcript.transcript_id = object_xref.ensembl_id AND object_xref.ensembl_object_type = 'Transcript' AND object_xref.xref_id = xref.xref_id AND xref.external_db_id = external_db.external_db_id AND external_db.db_name = 'RefSeq_mRNA';"


Also, I was trying to play around with the databases schema but I am not able to find any solution to problem.

Ultimately, I wish to obtain a table like the following:

Gene stable ID      Transcript stable ID    Protein stable ID   RefSeq match transcript
ENSG00000120329     ENST00000239451         ENSP00000239451     NM_031947.4
ENSG00000164219     ENST00000419445         ENSP00000404676     NM_005023.4
ENSG00000150594     ENST00000280155         ENSP00000280155     NM_000681.4
ENSG00000113578     ENST00000337706         ENSP00000338548     NM_000800.5


Thank you in advance.
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.