You can use the standard apply
function:
df=data.frame(x=c("l","m",NA,NA,"p"),y=c(NA,"b","c",NA,NA),z=c("u",NA,"w","x","y"))
df2 = as.data.frame(t(apply(df,1, function(x) { return(c(x[!is.na(x)],x[is.na(x)]) )} )))
colnames(df2) = colnames(df)
> df
x y z
1 l <NA> u
2 m b <NA>
3 <NA> c w
4 <NA> <NA> x
5 p <NA> y
> df2
x y z
1 l u <NA>
2 m b <NA>
3 c w <NA>
4 x <NA> <NA>
5 p y <NA>