In order to do hierarchical clustering, you first require some measure of distance/similarity between your sequences.
By this I mean the following:
Given a set of sequences N, compute the pairwise distance between each sequence s, in N and all other sequences in N. This will allow you to create a distance matrix that will subsequently be clustered.
R gives a range of possibilities for generating distances matrices, e.g., Euclidean, Manhattan, etc. These may not be suitable for measuring the distance between sequences. Perhaps the hamming distance or some measure of pairwise conservation (depending on what you wish to explore using the clusters) will be more appropriate.
My guess is that you will have to generate your own custom distance matrix using an appropriate measure for your data and then do hierarchical clustering.
Given a custom distance matrix X:
hc <- hclust(as.dist(X), method='average')
Note, you will have to choose amongst methods of hierarchical clustering, viz., single, average and complete.
Good tutorials on clustering in R are given below: