A Licensed Psychoanalyst is an American credential, notably used in New York State, for practitioners who have completed formal psychoanalytic training and are licensed to practise psychoanalysis independently as a distinct profession in its own right.
A demanding and unusually personal training
Training to become a Licensed Psychoanalyst is long, and unusually, requires the candidate to undergo their own personal analysis throughout the training itself, on the basis that understanding one's own unconscious patterns closely is essential to working safely and effectively with a client's. Most American states do not license psychoanalysis as a separate profession in the way New York does, so analysts practising elsewhere in the US typically work under a psychology, social work or medical licence instead.
The UK equivalent, and a note on intensity
In the UK, the equivalent practitioners register with the British Psychoanalytic Council or with UKCP. Psychoanalysis itself is considerably more intensive than psychodynamic therapy, often involving several sessions a week sustained over a number of years, reflecting the depth of work this particular approach is built around.