Madame Vastra

Partner with Jenny Flint (When this creature enters, target player may put Jenny Flint into their hand from their library, then shuffle.)
Madame Vastra must be blocked if able.
Whenever a creature dealt damage by Madame Vastra this turn dies, create a Clue token and a Food token.

Doctor Who

"Partner with [name]" represents two abilities. The first is a triggered ability: "When this permanent enters the battlefield, target player may search their library for a card named [name], reveal it, put it into their hand, then shuffle."

If Madame Vastra is blocking or being blocked by another creature and both of those creatures are dealt lethal combat damage at the same time, they each die at the same time and the last ability will trigger.

Note that the target player searches their library (which may be affected by effects such as that of Stranglehold) and that the card they find is revealed, even though these words aren't included in the ability's reminder text.

The second ability represented by the "partner with [name]" keyword modifies the rules for deck construction in the Commander variant and has no function outside of that variant. If a legendary creature card with "partner with [name]" is designated as your commander, the named legendary creature card can also be designated as your commander.