As part of her job, it is understood that the woman has access to information on criminal cases and sensitive files including cases linked to dissident republicans.
A source explained: "This is very much a cause for concern. This woman has been involved with a dissident republican organisation for a number of years.
"She is an advocate of the IRA, a strong supporter who encourages membership of what is an illegal organisation. Obviously she is not a suitable candidate for working in the law library."
The woman is not working as a solicitor but has been present when pre-case conferences and other sensitive meetings have taken place in the library.
The organisation that the woman is involved with was formed in 2007 and has been linked to a number of atrocities including the shooting of two British soldiers in 2009.
Among its members are Saoirse Breathnach (38) from Ballybrack, south Dublin, a well known dissident who was jailed for seven years in December 1998 along with four men for their part in an attempted bank holiday robbery during which a sixth raider was shot dead.
Breathnach was armed with an assault rifle during the raid in which her associate Ronan McLoughlin (28), from Ballymun, died when gardai opened fire.
Jailing the men, Mr Justice Frederick Morris said the court had no doubt that this was "a highly organised and premeditated crime and bore all the hallmarks of a paramilitary undertaking".
Sources say that the dissident group which the woman who works in the law library is linked to has "some support" in Dublin but is "strong" in Dundalk, Co Louth, as well as Derry and Belfast.
"Who she is involved with openly support Oglaigh na hEireann and advocate armed struggle. It would be a disaster if this woman has access to garda information on upcoming dissident cases," the source explained.
"While it would be wrong to call her an active terrorist, this lady is a supporter and facilitator of an illegal organisation," the source added.
The group which she supports also has links to the new republican paramilitary group calling itself the IRA, which is claiming responsibility for the murder of prison officer David Black earlier this month.
In a statement released yesterday, the group say the killing was in direct response to the conditions in Maghaberry Prison, where Mr Black worked.
Father-of-two Mr Black (52) was shot dead on the M1 in Co Armagh on November 1 as he drove to work.
The new organisation is a coalition of dissident groups formed earlier this year.