Hey there Michał thanks for reaching out and welcome to Clay!
Something like this would not currently be possible with Clay, due to the fact that this scenario will need to use a webhook in order to get the information into a Clay table and when it comes to webhooks any fields that are brought into a Clay table will have to be manually mapped out into columns from the source, which is what is preventing this from running automatically. Normally when a source is generated in a Clay table it will map out its data fields into columns and any enrichment that gets information from LinkedIn would automatically run whenever a new table is entered, because the values are going to be mapped out automatically allowing the enrichment to run by itself.
However since webhook don't do this as previously stated it would not be possible.