Naming ester as a substituent to carboxylic acid

Can carboxylic acid functional group -COOH and ester's functional group R-COO-R' be in one structure? If yes, carboxylic acid will be the parent chain and ester will be the substituent as c.a. is higher than ester in the priority table. Then, how do we name the structure where ester becomes a substituent? Thank you.

As you have correctly stated in the question, the $$\ce{-COOH}$$ group has higher priority than the $$\ce{-COOR}$$ group. In fact, the $$\ce{-COOH}$$ group has the highest priority (excepting cations) in IUPAC nomenclature.

The $$\ce{-COOH}$$ group should be included as the suffix of the parent chain, while the $$\ce{-COOR}$$ is indicated using a prefix.

In fact, Section P-65.6.3.2.2 of the Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names, 2013 (aka the Blue Book) specifies the rules for this.

When, in an ester with the general structure R-CO-O-R' or R-S(O)XO-R', another group is present that has priority for citation as the principal group or when all ester groups cannot be described by the methods prescribed for naming esters, an ester group is indicated by prefixes as 'acyloxy' for the group R-CO-O—, and 'alkyloxy(alkany1)...oxo' or 'alkyl(allcanyl)oxycarbonyl' for the group —CO-OR'.

I quote the example provided in the text:

And another one (not from the Blue Book though)

3-Ethoxy-3-oxopropanoic acid

References: Favre, H. A., Powell, W. H. Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 R. Soc. Chem 2013 DOI: 10.1039/9781849733069