# If you'd like to omit non-matching lines from the result; add ';d' to the end of the expression.
sed -E 's/^(?:[a-z\d]+-?)*?(?:\/|(?=20\d{2}-?){1,2})//gm;t' <<< "abc-def/something/else/ [incl. slash if there is not character before it]
abc-def-2019/something/else/
abc-def-2019-2020/something/else/
abc-def-125-2019/something/else/"
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for SED, please visit: https://www.gnu.org/software/sed/manual/html_node/The-_0022s_0022-Command.html