In theory if you know the medoids from the train clustering, you just need to calculate the distances to these medoids again in your test data, and assign it to the closest. So below I use the iris example:

    library(cluster)
    set.seed(111)
    idx = sample(nrow(iris),100)
    trn = iris[idx,]
    test = iris[-idx,]
    
    mdl = pam(daisy(iris[idx,],metric="gower"),3)

we get out the medoids like this:

    trn[mdl$id.med,]
        Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
    40           5.1         3.4          1.5         0.2     setosa
    100          5.7         2.8          4.1         1.3 versicolor
    113          6.8         3.0          5.5         2.1  virginica

So below I write a function to take these 3 medoid rows out of the train data, calculate a distance matrix with the test data, and extract for each test data, the closest medoid:

    predict_pam = function(model,traindata,newdata){
    
    nclus = length(mdl$id.med)
    DM = daisy(rbind(traindata[mdl$id.med,],newdata),metric="gower")
    max.col(-as.matrix(DM)[-c(1:nclus),1:nclus])
    
    }

You can see it works pretty well:

    predict_pam(mdl,trn,test)
     [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3
    [39] 3 3 3 3 3 3 3 3 3 3 3 3

We can visualize this:

    library(MASS)
    library(ggplot2)
    
    df = data.frame(cmdscale(daisy(rbind(trn,test),metric="gower")),
    rep(c("train","test"),c(nrow(trn),nrow(test))))
    colnames(df) = c("Dim1","Dim2","data")
    
    df$cluster = c(mdl$clustering,predict_pam(mdl,trn,test))
    df$cluster = factor(df$cluster)
    
    ggplot(df,aes(x=Dim1,y=Dim2,col=cluster,shape=data)) + 
    geom_point() + facet_wrap(~data)

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/0oyl7.png