If the first 2 tax periods have expired then you can submit a VD to claim the same. Fixed penalty can be imposed by the FTA and same is given in the Law. You need to see if it is beneficial to claim under the risk of a penalty.

And how about the input VAT claim amounting to less than or equal to AED 10,000 after the lapse of two tax periods? Whether that can be claimed through filing VD, as the VD can filed only when the tax impact is exceeding AED 10,000? The said clarification is silent about the said concurrency of provisions.

You are absolutely right. Clarification is silent.

The VD guide and Law does clarify...where the VAT implication is less than 10k you can submit a VD where there is no current return through which it can be rectified...in the case of input beyond 2 tax periods you cannot claim the same in current return ie there is no current return through which you can rectify this...so in effect you are entitled to submit a VD for missed out inputs below 10k

In a scenario where a taxable person has not recovered the input tax within two tax periods (and both conditions are satisfied), they will be required to submit a voluntary disclosure to recover the input VAT. Upon filing VD, an automatic fixed penalty will be levied which is AED 3,000 for first time and AED 5,000 on repetition. Percentage based penalty may not be levied as in the said scenario there will not be an unpaid due tax amount. It will be pertinent for a taxable person to undertake a cost-benefit analysis before filing a VD. Please note this treatment will be same even the input VAT is less than AED 10,000.