The OED has no entries relating to "recently released from prison", so I believe the answer to your question is No: there is no specific word. The closest entry is under released:
That has been released (in various senses); spec. (a) revoked or remitted (now chiefly Law); (b) set free or made available (also with modifying adverb) (now the commonest sense).
1894 Times 27 Aug. 4 Dr. Kenny, one of the recently-released suspects, presided.
2006 New Scientist 29 July 6/4 Prendergast's team studied released convicts in San Diego who had been treated in a prison therapeutic community.
I did find the word unprisoned, for which the single citation in OED is from Dickens' The Old Curiosity Shop:
Released from prison.
1841 Dickens Old Curiosity Shop ii. lii. 88 Perhaps not one of the unprisoned souls had been able [etc.].
Support agencies use a number of terms such as those listed in the related question. Step Ahead and the Minnesota Department of Corrections use newly-released ex-offender:
Finding a job is an important part of transition after incarceration. Ideally, you will find a job that matches your skills and interests. The reality is that the first jobs many newly released ex-offenders find do not match their desired careers.