You simply assign the axis on which you want to plot as input to the function and explicitly specify on which axis you want to plot in sns.lineplot

import pandas as pd
import numpy as np
import seaborn as sns
from matplotlib import pyplot as plt

def plotf(df_x,ax):
    g = sns.lineplot(data=df_x[['2016','2017','2018']],ax=ax)
    g.set_xticks(range(0,12))
    g.set_xticklabels(['Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec','Jan'])
    return g

df = pd.DataFrame({'Period': list(range(1,13)),
                           '2016': np.random.randint(low=1, high=100, size=12),
                           '2017': np.random.randint(low=1, high=100, size=12),
                           '2018': np.random.randint(low=1, high=100, size=12)}) 

fig, ax = plt.subplots(nrows=3)
plotf(df,ax[0])
plotf(df,ax[1])
plotf(df,ax[2])