It has occurred to me that there is actually a small flaw in what most of us, including me, have said to you. If there was an agreement that you would have no lodger, and you did take one on, it would be reasonable I believe for the landlord to claim some small damage under 'increased normal wear and tear'. Normal wear and tear is built into the rent, and cannot be charged for in the security deposit. But there is a case that a landlord could charge for increased normal wear and tear for lodgers that are forbidden by contract. But in any case this should be small. I don't know what would be considered reasonable, but certainly only a very small fraction of monthly rent. Off the top of my head, I'd say any claim of more than 5% of the monthly rent would be excessive for that, and that may be too high.
The landlord could have some basis to claim this, but since you have won my sympathy against a party which is not earning my sympathy, I would suggest that you do not help them in making this claim. For your part, simply stick to the case that there was no damage done by the lodger, and therefore nothing to be paid.
>> I told her that I will be renting one room for some time and she did not say anything against it.
That qualifies as acquiescence to me. A contract-party is not allowed to acquiesce in appearance, while quietly storing up a notion of breach to hit you with later; that would be unreasonable and bad-faith behavior. The law solves this problem by taking a view of acquiescence as equivalent to the contract being tacitly amended with the consent of both parties--so there is no breach.
>> How can she prove that damages were done by me if new tenants are living in the property for 3 months?
There is never any true proof in any area of law. One's task is to convince the judge/jury/adjudicator (the PRTB in this case) under the evidence that you are allowed to present.
There is a common fallacy among Irish people that 'it is her word against mine' means that the words cancel out in the eyes of the court, and maybe also that then only hard physical evidence or records matter. This is wrong. Testimony is evidence, and it gets weight. Credibility affects the weight of evidence. The standard in a civil matter like this is preponderance of the evidence--the PRTB should decide which of the two cases --your case (that you did not damage the stuff) and the landlord's case (that you did) is more likely to be true.
Assuming you have told us the relevant facts, your landlord should be in serious trouble in this regard, assuming an intelligent adjudicator. Because the landlord's credibility is seriously damaged.
Just put the full story on front of the PRTB. Tell the PRTB that you told the landlord about the lodger, and give an approximate date if available, and how the landlord did not object, etc.
And then how you were first told that the deposit was being taken for 'breach of contract' because of the lodger. And how the landlord changed the story to one of damaged property but only after you got advice that no retention of deposit should follow from breach of contract related to the lodger, and how all this happened after a long delay.
Assuming you have presented all the relevant evidence, and the adjudicator is reasonable and intelligent, I think you have an excellent chance of prevailing over the landlord.