I haven't suggested the above as an answer, because it's a bit wordy. However, the references below indicate that this isn't necessarily either string-pulling or cronyism, though it could include both of the above. It would include a situation that I was once in where I was recommended for a job by a neighbour of a cousin of mine who knew someone in another department of her workplace was looking for someone to fill a post. It wasn't string-pulling, because I hadn't asked to be recommended and didn't know that she'd recommended me until I got a letter inviting me to an interview. It wasn't cronyism, because my cousin hadn't asked her neighbour to do it and I hardly knew the neighbour. The neighbour also barely knew the person who needed to recruit for the position. It was, however, not very ethical because as the job was never advertised and I was the only person who was considered for it. That was completely against equality of opportunity and diversity. It was a very long time ago, and yes I got the job, though the job was adapted (and upgraded) to suit how the recruiter thought I could best fit in to the department, which was also not good HR practice, though it worked very well for both of us and the department at the time.

" “Avoir du piston”, “avoir un piston”, “avoir un coup de piston”, autant d’expressions qui veulent dire « avoir une personne qui nous pousse pour obtenir quelque chose » par son réseau ou par sa fonction dans l’entreprise.
...
"D’un point de vue RH, le piston, bien qu’encore très répandu, n’a pas la part belle. « Le piston, c’est favoriser le recrutement de quelqu’un parce qu’il connaît quelqu’un. Et cela arrive très régulièrement de recevoir des CV par réseau, de personnes recommandant un ami ou un membre de leur famille. La pratique en tant que telle est discriminante et dangereuse pour l’entreprise car elle pousse à recruter des profils qui viennent d’environnements familiers pour les mauvaises raisons, au détriment de critères objectifs. C’est une pratique peu éthique et contraire aux engagements d’un bon RH. » nous livre Stella W., head of talent."

"Le piston est l'action par laquelle une personne est recrutée pour un emploi ou nommée à une fonction grâce à la recommandation ou l'appui1 d'une connaissance qui, travaillant souvent au sein de l'entreprise ou de l'organisation concernée, va recommander le candidat à l'employeur ou à l'institution.

L'employeur valide généralement les compétences du candidat recommandé avant de l'employer. "

cro·ny·ism
/ˈkrōnēˌizəm/

nounDEROGATORY
the appointment of friends and associates to positions of authority, without proper regard to their qualifications.
"it looked like an end to the cronyism with which many of the government's appointments had been tainted"

the situation in which someone important gives jobs to friends rather than to independent people who have the necessary skills and experience
https://dictionary.cambridge.org/us/dictionary/english/crony...